Colouring random graphs and maximising local diversity

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.Comment: 10 pages, 10 figure

Chronic helminth infection burden differentially affects haematopoietic cell development while ageing selectively impairs adaptive responses to infection

Throughout the lifespan of an individual, the immune system undergoes complex changes while facing novel and chronic infections. Helminths, which infect over one billion people and impose heavy livestock productivity losses, typically cause chronic infections by avoiding and suppressing host immunity. Yet, how age affects immune responses to lifelong parasitic infection is poorly understood. To disentangle the processes involved, we employed supervised statistical learning techniques to identify which factors among haematopoietic stem and progenitor cells (HSPC), and both innate and adaptive responses regulate parasite burdens and how they are affected by host age. Older mice harboured greater numbers of the parasites’ offspring than younger mice. Protective immune responses that did not vary with age were dominated by HSPC, while ageing specifically eroded adaptive immunity, with reduced numbers of naïve T cells, poor T cell responsiveness to parasites, and impaired antibody production. We identified immune factors consistent with previously-reported immune responses to helminths, and also revealed novel interactions between helminths and HSPC maturation. Our approach thus allowed disentangling the concurrent effects of ageing and infection across the full maturation cycle of the immune response and highlights the potential of such approaches to improve understanding of the immune system within the whole organism

From one solution of a 3-satisfiability formula to a solution cluster: Frozen variables and entropy

A solution to a 3-satisfiability (3-SAT) formula can be expanded into a cluster, all other solutions of which are reachable from this one through a sequence of single-spin flips. Some variables in the solution cluster are frozen to the same spin values by one of two different mechanisms: frozen-core formation and long-range frustrations. While frozen cores are identified by a local whitening algorithm, long-range frustrations are very difficult to trace, and they make an entropic belief-propagation (BP) algorithm fail to converge. For BP to reach a fixed point the spin values of a tiny fraction of variables (chosen according to the whitening algorithm) are externally fixed during the iteration. From the calculated entropy values, we infer that, for a large random 3-SAT formula with constraint density close to the satisfiability threshold, the solutions obtained by the survey-propagation or the walksat algorithm belong neither to the most dominating clusters of the formula nor to the most abundant clusters. This work indicates that a single solution cluster of a random 3-SAT formula may have further community structures.Comment: 13 pages, 6 figures. Final version as published in PR

Statistical Confirmation of a Stellar Upper Mass Limit

We derive the expectation value for the maximum stellar mass (m_max) in an ensemble of N stars, as a function of the IMF upper-mass cutoff (m_up) and N. We statistically demonstrate that the upper IMF of the local massive star census observed thus far in the Milky Way and Magellanic Clouds clearly exhibits a universal upper mass cutoff around 120 - 200 M_sun for a Salpeter IMF, although the result is more ambiguous for a steeper IMF.Comment: PDF, 5 pages, 4 figures. Accepted to the Astrophysical Journal Letter

Topology of multiple log transforms of 4-manifolds

Given a 4-manifold X and an imbedding of T^{2} x B^2 into X, we describe an algorithm X --> X_{p,q} for drawing the handlebody of the 4-manifold obtained from X by (p,q)-logarithmic transforms along the parallel tori. By using this algorithm, we obtain a simple handle picture of the Dolgachev surface E(1)_{p,q}, from that we deduce that the exotic copy E(1)_{p,q} # 5(-CP^2) of E(1) # 5(-CP^2) differs from the original one by a codimension zero simply connected Stein submanifold M_{p,q}, which are therefore examples of infinitely many Stein manifolds that are exotic copies of each other (rel boundaries). Furthermore, by a similar method we produce infinitely many simply connected Stein submanifolds Z_{p} of E(1)_{p,2} # 2(-CP^2)$ with the same boundary and the second Betti number 2, which are (absolutely) exotic copies of each other; this provides an alternative proof of a recent theorem of the author and Yasui [AY4]. Also, by using the description of S^2 x S^2 as a union of two cusps glued along their boundaries, and by using this algorithm, we show that multiple log transforms along the tori in these cusps do not change smooth structure of S^2 x S^2.Comment: Updated, with 17 pages 21 figure

Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random Satisfiability problem, and its application to stop-and-restart resolutions

A large deviation analysis of the solving complexity of random 3-Satisfiability instances slightly below threshold is presented. While finding a solution for such instances demands an exponential effort with high probability, we show that an exponentially small fraction of resolutions require a computation scaling linearly in the size of the instance only. This exponentially small probability of easy resolutions is analytically calculated, and the corresponding exponent shown to be smaller (in absolute value) than the growth exponent of the typical resolution time. Our study therefore gives some theoretical basis to heuristic stop-and-restart solving procedures, and suggests a natural cut-off (the size of the instance) for the restart.Comment: Revtex file, 4 figure

Deleterious consequences of antioxidant supplementation on lifespan in a wild-derived mammal

Peer reviewedPublisher PD

Behavior of heuristics and state space structure near SAT/UNSAT transition

We study the behavior of ASAT, a heuristic for solving satisfiability problems by stochastic local search near the SAT/UNSAT transition. The heuristic is focused, i.e. only variables in unsatisfied clauses are updated in each step, and is significantly simpler, while similar to, walksat or Focused Metropolis Search. We show that ASAT solves instances as large as one million variables in linear time, on average, up to 4.21 clauses per variable for random 3SAT. For K higher than 3, ASAT appears to solve instances at the ``FRSB threshold'' in linear time, up to K=7.Comment: 12 pages, 6 figures, longer version available as MSc thesis of first author at http://biophys.physics.kth.se/docs/ardelius_thesis.pd

Focused Local Search for Random 3-Satisfiability

A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of focusing the local moves on the presently unsatisfiedclauses is known to be very effective: the time to solution has been observed to grow only linearly in the number of variables, for a given clauses-to-variables ratio $\alpha$ sufficiently far below the critical satisfiability threshold $\alpha_c \approx 4.27$. We present numerical results on the behaviour of three focused local search algorithms for this problem, considering in particular the characteristics of a focused variant of the simple Metropolis dynamics. We estimate the optimal value for the ``temperature'' parameter $\eta$ for this algorithm, such that its linear-time regime extends as close to $\alpha_c$ as possible. Similar parameter optimisation is performed also for the well-known WalkSAT algorithm and for the less studied, but very well performing Focused Record-to-Record Travel method. We observe that with an appropriate choice of parameters, the linear time regime for each of these algorithms seems to extend well into ratios $\alpha > 4.2$ -- much further than has so far been generally assumed. We discuss the statistics of solution times for the algorithms, relate their performance to the process of ``whitening'', and present some conjectures on the shape of their computational phase diagrams.Comment: 20 pages, lots of figure

Lifelongα-tocopherol supplementation increases the median life span of C57BL/6 mice in the cold but has only minor effects on oxidative damage

The effects of dietary antioxidant supplementation on oxidative stress and life span are confused. We maintained C57BL/6 mice at 7 ± 2°C and supplemented their diet with α-tocopherol from 4 months of age. Supplementation significantly increased (p = 0.042) median life span by 15% (785 days, n = 44) relative to unsupplemented controls (682 days, n = 43) and also increased maximum life span (oldest 10%, p = 0.028). No sex or sex by treatment interaction effects were observed on life span, with treatment having no effect on resting or daily metabolic rate. Lymphocyte and hepatocyte oxidative DNA damage and hepatic lipid peroxidation were unaffected by supplementation, but hepatic oxidative DNA damage increased with age. Using a cDNA macroarray, genes associated with xenobiotic metabolism were significantly upregulated in the livers of female mice at 6 months of age (2 months supplementation). At 22 months of age (18 months supplementation) this response had largely abated, but various genes linked to the p21 signaling pathway were upregulated at this time. We suggest that α-tocopherol may initially be metabolized as a xenobiotic, potentially explaining why previous studies observe a life span extension generally when lifelong supplementation is initiated early in life. The absence of any significant effect on oxidative damage suggests that the life span extension observed was not mediated via any antioxidant properties of α-tocopherol. We propose that the life span extension observed following α-tocopherol supplementation may be mediated via upregulation of cytochrome p450 genes after 2 months of supplementation and/or upregulation of p21 signaling genes after 18 months of supplementation. However, these signaling pathways now require further investigation to establish their exact role in life span extension following α-tocopherol supplementation